Space of modular forms of level 10 and weight 38

• Label: 10.38
• Level: 10
• Weight: 38
• Dimension: 29
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 228
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	=	\( 38 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(228\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{38}(\Gamma_1(10))\).

	Total	New	Old
Modular forms	115	29	86
Cusp forms	107	29	78
Eisenstein series	8	0	8

Trace form

29 * q - 262144 * q^2 - 101265596 * q^3 - 481036337152 * q^4 - 6507646614635 * q^5 + 44703658541056 * q^6 - 8136610409482472 * q^7 - 18014398509481984 * q^8 - 2304638159578360651 * q^9 - 1521086920865873920 * q^10 - 47358817471646852612 * q^11 - 6958918768479174656 * q^12 + 909184511023571927314 * q^13 + 6885216098525646946304 * q^14 + 11262146394346719077380 * q^15 + 136948628003219711197184 * q^16 - 156847220844825553473882 * q^17 + 143600426236374980231168 * q^18 + 1123235372831685947206420 * q^19 - 77085929859480960368640 * q^20 + 13423560292316208490591408 * q^21 - 1373747344466365658431488 * q^22 - 39511609522513754583347496 * q^23 + 61234507168461358935048192 * q^24 + 81378403033802651447910725 * q^25 - 53650253576171325522182144 * q^26 + 10245242176817474957683960 * q^27 - 559143609744326168403771392 * q^28 + 3712969820303538001277311110 * q^29 - 4932811537572296068080599040 * q^30 + 25149584229816964770142061248 * q^31 - 1237940039285380274899124224 * q^32 + 21753087921420048362119123008 * q^33 + 8666327145830095961143640064 * q^34 + 119961139532741980183954742840 * q^35 + 191818087012985903660937510912 * q^36 + 187071649912861757278571509978 * q^37 - 361112668985263133933935001600 * q^38 - 294857222528293705116244690312 * q^39 - 32910656200123704178250874880 * q^40 + 1500207025340633175037380562378 * q^41 - 3387625646236979152701177724928 * q^42 - 162888835175696745465335348276 * q^43 + 2032341358202155880304519151616 * q^44 - 10195286500654818957532879137195 * q^45 - 10154175730363847857844093190144 * q^46 + 17251738736487345234779042140848 * q^47 - 478213256418218412873472802816 * q^48 + 16500442237825440486637383747441 * q^49 - 70076772812872198318273023180800 * q^50 - 34405000338976265177014080565912 * q^51 + 62478683854015886606677105967104 * q^52 - 59277127589292161917743812257686 * q^53 + 669590887750726994638019242229760 * q^54 - 327363832948673712288879759102420 * q^55 - 15857151144895945023458837004288 * q^56 + 211651039157794433062940140199600 * q^57 - 81658069382197038522402023669760 * q^58 + 3510989143377458447747302262565820 * q^59 - 1492478616246583643555942293831680 * q^60 + 4303429342530410139168895893131038 * q^61 + 669747197889664786812960224837632 * q^62 - 7056364533093793760838850782630616 * q^63 - 2271629875608987087482092144033792 * q^64 - 28996931732624245715609127990184070 * q^65 - 7086505546979866725370564148461568 * q^66 - 14834478129506952863355414739088252 * q^67 - 10778458943952243887926758082609152 * q^68 + 72765357677504128155178578244182208 * q^69 - 23709495111498643874544244458782720 * q^70 + 99884354267595480949252405647475368 * q^71 + 9868146150030254490968209278107648 * q^72 + 17162246578778779758533141811531214 * q^73 + 38724102869700225365520303790751744 * q^74 - 43513342065867213359063224135156300 * q^75 + 73388440590241829078109278363975680 * q^76 - 370837541095491940327721215526630544 * q^77 + 281686233996506324613321821557620736 * q^78 - 137224808550975719181179115950769200 * q^79 - 30731492255312438394912305536040960 * q^80 + 528029635327291558644714386388067269 * q^81 + 147587241779774488519290812282437632 * q^82 + 320926720613963505679306276287863844 * q^83 - 791114606211971007422027006774083584 * q^84 + 1407498958050928306519017014253008190 * q^85 - 1250077272128920277829636038190956544 * q^86 + 1388952154489028011605118115175443160 * q^87 - 94403198679198193199051961865863168 * q^88 - 6539770640742030132472318014317498830 * q^89 + 5268777432845490064171491318461890560 * q^90 + 263918224653646306256225478299262608 * q^91 - 2715217131384300026330361624375853056 * q^92 + 6623305052922340495062522712944463088 * q^93 + 2993282069520458819103527513163300864 * q^94 - 5707305304659879378820653974836045100 * q^95 + 211107058755932197969921660709502976 * q^96 + 19574454273022155120560716121395075078 * q^97 - 5220610730153960440690972725497561088 * q^98 + 60040782278343924911960853362672656508 * q^99

Decomposition of \(S_{38}^{\mathrm{new}}(\Gamma_1(10))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
10.38.a	\(\chi_{10}(1, \cdot)\)	10.38.a.a	2	1
		10.38.a.b	3
		10.38.a.c	3
		10.38.a.d	3
10.38.b	\(\chi_{10}(9, \cdot)\)	10.38.b.a	18	1

Decomposition of \(S_{38}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{38}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{38}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{38}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{38}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{38}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)